Slope Intercept Form

Image result for linear functions cartoon

Much of our time in 8th grade is spend analyzing the characteristics of linear functions.  Linear functions are very useful in the “real world,”  and understanding how they work is an important key to understanding any relationship between two changing quantities.

A linear equation has four parts: an independent variable, a dependent variable, slope and a y-intercept.  Students are first introduced to these parts through the use of slope-intercept form.

Image result for slope intercept form

In 8th grade, the equation y = mx + b is most often used to represent linear functions.  The variable x represents an input value, and the variable y represents an output value.  The variable m, represents the rate of change between the inputs and outputs, or the slope of the relationship.

We first investigate slope of a graph, by measuring the differences horizontally and vertically between two points.

Image result for slope rise over run

We then move to finding those differences between two points by using subtraction.

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Finally, we use the slope formula to calculate the slope without having to use a graph.

Image result for slope formula

Don’t think we forgot about the last part of a linear function!  The y-intercept is simply the coordinates of the point where the graphed line crosses the y-axis.  It is represented by the b in slope-intercept form.

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Image result for y-intercept

To learn more about slope, click here.  Try finding slope from a graph here, and slope from two points here.  Try identifying the parts of a linear equation in slope intercept form here.  Good luck!

 

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